A comment posted by a reader on a recent post reprimanded me for suggesting that marijuana caused relationships to go bad. While in that instance the reader was mistaken, as I had specifically used the word associated, the comment made me think that maybe I should explain the differences here. I'm a scientist studying addiction, and in the field, it's very important to be clear about what each of the words you use means.

So let's get into it:

Correlation - When researchers find a correlation, which can also be called an association, what they are saying is that they found a relationship between two, or more, things. For instance, in the case of the marijuana post, the researchers found an association between using marijuana as a teen, and having more troublesome relationship in mid, to late, twenties.The trouble is, there could be other things affecting this relationship that the researchers don't know about, but read on.

Causation - When an article says that causation was found, this means that the researchers are saying that changes in one thing they measured directly cause changes in the other. An example would be research showing that jumping of a clifff directly causes great physical damage.

Most of the research you read about indicates a correlation between variables, not causation. You can find the key words by carefully reading. If the article says something like "men were found to have," or "women were more likely to," they're talking about associations, not causation.

Why the difference?

The reason is that in order to actually be able to claim causation, the researchers have to split the participants into different groups, have some participants engage in the activity they want to study (like taking a new drug), while the rest don't. This is in fact what happens in clinical trials of medication because the FDA requires proof that the medication actually makes people better. Obviously, it is much more difficult to prove causation than it is to prove an association.

So should we ignore correlations?

No! Correlations are still important and still need to be looked at, especially in some areas of research like addiction. We can't randomly give people drugs like methamphetamine as children and study their brain development to see how the stuff affects them, that would be unethical. So what we're left with is a need to study what meth use (and use of other drugs) is associated with. It's for this reason that researchers use special statistical methods to assess associations, making certain that they are also considering other things that may be interfering with their results.

In the case of the marijuana article, the researchers ruled out a number of other interfering variables known to affect relationships, like aggression, gender, education, closeness with other family members, etc. By doing so, they did their best to assure that the association found between marijuana and relationship status was real. As more researchers assess this relationship in different ways, we'll learn more about its true nature.

This is how we found out that smoking causes cancer. Through endlessly repeated findings showing an association. That turned out pretty well, I think...

Basically, I was approached a few months ago by a senior editor of Symantec's online magazine "Norton Today" because they were interested in doing a piece on Art and Security. I was approached because of my old work in security data visualization and the fact that'd I'd started to rework and hang the pieces in art shows like Artomatic and My Space on 7th.

Anyway, the interview went really well (in addition to being a lot of fun) and it's now online at:

http://nortontoday.symantec.com/features/articles/art_of_security.php

They used a few older images in their Flash slideshow (My fault - I didnt get them newer images in time).  These were the originals we used at NetSec to do analysis and which have been in a number of presentations (and were in the batch I sent to ArcSight as examples when they were still developing Interactive Discovery, iirc).   

You can find the "art" versions that I've hung up in galleries at the following link:

http://sintixerr.wordpress.com/art-versions-of-data-visualizations/

I'm still interested in working more of these, but have been moving from graphing - which was a necessity of the business at the time - into a broader field of ontological information/concept representation in art.

(This is in addition to my media experimentation with / interest in projection. I think Id like to merge these two tracks together in the future, but havent gotten there yet.)

So, what do scientists do, anyway?

The easy answer is simply to say that scientists ‘do science’, which means it is the process of science that is held in common by all scientists.  This process is used to answer questions through the production and analysis of data.

What is the process scientists use to produce their data?  Generally, they collect their data using two powerful tools: carefully designed observational studies and experiments.

Observational Studies

The usual purpose of observational studies (also known as descriptive studies) is to describe phenomena; for example, its average value and the amount of its variability.  The study of obesity in adult males of a particular city would be an example of an observational study.  We would expect that study to report the mean amount of male obesity, the amount of variability in obesity, and how obesity varies (e.g., whether the distribution of obesity among adult males is normal, skewed, etc. http://www.cvgs.k12.va.us/DIGSTATS/main/descriptv/d_skewd.html ).

Descriptive studies can become quite complicated.  A study on adult male obesity might include separate results for young, middle-aged and elderly men; that study would use stratified sampling (http://www.coventry.ac.uk/ec/~nhunt/meths/strati.html ).  Furthermore, several variables might be studied—e.g., blood pressure, blood cholesterol levels, amount of body fat, amount of daily exercise, daily caloric intake and amount of heart disease—and their averages and variability reported. 

The study also might tell you how these variables are associated with each other.  That is, do men with greater than average amounts of body fat have higher blood pressure? Do these men tend to exercise more or less than men with less body fat?  Do they have more or less heart disease than those men with less body fat?  Scientists use correlation analysis to answer these questions. (You can learn about correlation analysis here— http://www.geniq.net/res/correlation-coefficient-max-values-less-than-one.html .)

Observational studies cannot tell you about the ‘cause and effect’ relationship between two variables.  For example, one cannot prove that smoking cigarettes causes cancer using an observational study.  Neither can one prove—using an observational study—that a high degree of obesity causes heart disease.  The best one can do with an observational study is to demonstrate the relationships among variables (e.g., high rates of smoking are associated with high rates of cancer). This is because an observational study cannot rule out the possibility that two variables (e.g., smoking and cancer) are linked together through an association with a third, as yet unknown, variable that causes the original two variables to vary.

An example might shed some more light on this limitation.  An enterprising gentleman from the island of Nantucket collected this data on the local population: ice cream consumption and number of drownings.  He was surprised to notice that the correlation between ice cream consumption and drowning was strongly positive, meaning that the more ice cream one consumed the greater one’s chance of drowning!  Was the consumption of ice cream causing drowning?  Alarmed, he took his evidence to the local public health officer.

The officer smiled and said, “Of course, it also might be that when the temperature gets hotter people tend to eat more ice cream and swim more in the ocean, than when the temperature is cooler.  More people swimming means more chances of drowning.” 

Temperature, in the Case of the Deadly Ice Cream, was a lurking variable.  That is, it was an undetected variable whose relationship with the two variables of interest was significant. [When lurking variables are detected, the partial correlation coefficient can be used to remove their effects. (http://www2.chass.ncsu.edu/garson/pa765/partialr.htm , www.ajronline.org/cgi/reprint/185/1/3.pdf .)]

The problem with even well-designed observational studies is that there is no way to be certain they are free of lurking variables.  The descriptions these observational studies provide, nonetheless, are accurate. However determination of cause and effect is impossible. (Furthermore, even when lurking variables are absent, a correlation may be due to chance and not indicate a causal relationship.) Experiments must be used to determine causal relationships—e.g., between smoking cigarettes and cancer.

Experiments

The key difference between an experiment and an observational study is that, in an experiment, treatments are randomly assigned to the experimental units or subjects.  This difference is what allows us to infer that one variable has a causal relationship with another variable.

That means experiments always must have at least two variables: an independent variable and a dependent variable.  The independent variable is the treatment; the experimenter manipulates the level of this variable and observes the changes caused, if any, in the dependent variable.   The experimenter attempts to control or hold all other variables constant so that they do not confound his results.

For example, our enterprising gentleman, skeptical of the Public Health Officer’s explanation, decided to do an experiment.  He planned to randomly select two groups of 50 Nantucketians.  Group A would be given an ice cream bar; Group B would be given a candy bar.  One-hour after eating, the 100 Nantucketians (i.e., the experiment's subjects) would swim fifty yards into the ocean and another fifty yards back to the beach—while rescuers on jet skis patrolled nearby (the jet-skiers do not know which group a subject belongs to).  He reasoned that if ice cream were causing the drowning, then he should observe more Group ‘A’ than Group ‘B’ swimmers get into trouble.

Why are lurking variables not an issue, here?  At first glance it might seem that the answer is the ambient temperature does not vary because all 100 Nantucketians did the experiment at the same time.  Since temperature doesn’t vary, it cannot influence the outcome. True; however, even other undetected lurking variables are eliminated as possible confounding influences.  This is because the independent variable (the treatment) is manipulated by the experimenter—the experimenter randomly assigns the treatment levels (i.e., ice cream or candy) to the subjects.  This breaks any connection the treatment might otherwise have with another variable (e.g., temperature) and allows the experimenter to infer that variation in the independent variable is causing variation in the dependent variable.

Suppose that our enterprising gentleman finds that 10 subjects from Group ‘A’ need to be rescued by the jet-skiers, but only 4 subjects from Group ‘B’ need rescue.  Would that be enough to demonstrate that ice cream causes drowning?

Not quite, because it is possible the experiment was not run properly or it may be that, by chance, treatment ‘A’ got more weak swimmers than treatment ‘B’.  He needs to replicate the experiment to conclusively demonstrate a difference between the two treatments.  That means, on another day, he should repeat the experiment with a different set of 100 subjects.  It is unlikely that by chance alone, again, those swimmers assigned treatment ‘A’ are weaker than than those assigned treatment ‘B’.  Depending on budgets and resources, many scientists prefer to perform their experiments at least three times (i.e., three replications) and average the results of the replicates.

Ultimately, the experiment needs to be replicated by a different experimenter to be completely confident that the results indicate causation.  Why? Perhaps our enterprising gentleman was sub-consciously introducing a bias into the experiment that favored one treatment over another.

So, the three great principles of experiments—random assignment of treatments to subjects, control of all other variables, and replication—are what enable experimenters to infer ‘cause and effect’.

Sometimes it can be difficult to tell whether an investigation is an observational study or an experiment.  When in doubt, ask yourself if the levels of at least one of the variables studied are randomly assigned to the subjects.  If so, then it likely is an experiment; if not, it is an observational study.

This website gives more details about experimental design:

http://www.okstate.edu/ag/agedcm4h/academic/aged5980a/5980/newpage2.htm

Statistics for Experimenters by Box, Hunter & Hunter is an excellent book on the subject and not very technical--- http://www.amazon.com/Statistics-Experimenters-Introduction-Analysis-Building/dp/0471093157

Source: NSC; Note: No published data available for 1994Q3 to 1996Q4; No raw steel imports planned for 1999Q4.

The following example comes from Bartholomew et al. "The Analysis and Interpretation of Multivariate Data for Social Scientists."

It is an excellent example with which to wrap up PCA / FA. (There's a lot we haven't done, but it's almost time for me to move on.)

The example is "employment in 26 European countries", "eurojob" for short, from chapter 5 (either 1st or 2nd edition), and data for both editions is available at http://www.cmm.bris.ac.uk/team/amssd.shtml . Please note that I am using the 1st edition of the book, and the 1st edition data.

When I first worked this example, I knew that something interesting happened, but not why; and, there was one thing I didn't understand at all, back then.

One reason why this example is so good is that they provide both the data and a correlation matrix. In fact, most of their analyses in chapter 5 seem to be based on the correlation matrix, except in those few cases when they compute scores (for which they need the data). We get to return to our starting point, using the correlation matrix.

Here’s the raw data.

$latex data = \left(\begin{array}{lllllllll} 3.3 & 0.9 & 27.6 & 0.9 & 8.2 & 19.1 & 6.2 & 26.6 & 7.2 \\ 9.2 & 0.1 & 21.8 & 0.6 & 8.3 & 14.6 & 6.5 & 32.2 & 7.1 \\ 10.8 & 0.8 & 27.5 & 0.9 & 8.9 & 16.8 & 6. & 22.6 & 5.7 \\ 6.7 & 1.3 & 35.8 & 0.9 & 7.3 & 14.4 & 5. & 22.3 & 6.1 \\ 23.2 & 1. & 20.7 & 1.3 & 7.5 & 16.8 & 2.8 & 20.8 & 6.1 \\ 15.9 & 0.6 & 27.6 & 0.5 & 10. & 18.1 & 1.6 & 20.1 & 5.7 \\ 7.7 & 3.1 & 30.8 & 0.8 & 9.2 & 18.5 & 4.6 & 19.2 & 6.2 \\ 6.3 & 0.1 & 22.5 & 1. & 9.9 & 18. & 6.8 & 28.5 & 6.8 \\ 2.7 & 1.4 & 30.2 & 1.4 & 6.9 & 16.9 & 5.7 & 28.3 & 6.4 \\ 12.7 & 1.1 & 30.2 & 1.4 & 9. & 16.8 & 4.9 & 16.8 & 7. \\ 13. & 0.4 & 25.9 & 1.3 & 7.4 & 14.7 & 5.5 & 24.3 & 7.6 \\ 41.4 & 0.6 & 17.6 & 0.6 & 8.1 & 11.5 & 2.4 & 11. & 6.7 \\ 9. & 0.5 & 22.4 & 0.8 & 8.6 & 16.9 & 4.7 & 27.6 & 9.4 \\ 27.8 & 0.3 & 24.5 & 0.6 & 8.4 & 13.3 & 2.7 & 16.7 & 5.7 \\ 22.9 & 0.8 & 28.5 & 0.7 & 11.5 & 9.7 & 8.5 & 11.8 & 5.5 \\ 6.1 & 0.4 & 25.9 & 0.8 & 7.2 & 14.4 & 6. & 32.4 & 6.8 \\ 7.7 & 0.2 & 37.8 & 0.8 & 9.5 & 17.5 & 5.3 & 15.4 & 5.7 \\ 66.8 & 0.7 & 7.9 & 0.1 & 2.8 & 5.2 & 1.1 & 11.9 & 3.2 \\ 23.6 & 1.9 & 32.3 & 0.6 & 7.9 & 8. & 0.7 & 18.2 & 6.7 \\ 16.5 & 2.9 & 35.5 & 1.2 & 8.7 & 9.2 & 0.9 & 17.9 & 7. \\ 4.2 & 2.9 & 41.2 & 1.3 & 7.6 & 11.2 & 1.2 & 22.1 & 8.4 \\ 21.7 & 3.1 & 29.6 & 1.9 & 8.2 & 9.4 & 0.9 & 17.2 & 8. \\ 31.1 & 2.5 & 25.7 & 0.9 & 8.4 & 7.5 & 0.9 & 16.1 & 6.9 \\ 34.7 & 2.1 & 30.1 & 0.6 & 8.7 & 5.9 & 1.3 & 11.7 & 5. \\ 23.7 & 1.4 & 25.8 & 0.6 & 9.2 & 6.1 & 0.5 & 23.6 & 9.3 \\ 48.7 & 1.5 & 16.8 & 1.1 & 4.9 & 6.4 & 11.3 & 5.3 & 4.\end{array}\right)$

I remark that the matrix is 26x9. What we have is: for 26 countries, the % of people employed in 9 categories (agriculture, mining, etc.).

This would be a good, rather than excellent, example to end with simply because it takes us back to our roots, using the correlation matrix for its PCA analysis. I compute the correlation matrix, and I save it; but I also round it to 2 places, and show it to you:

$latex \left(\begin{array}{lllllllll} 1. & 0.04 & -0.67 & -0.4 & -0.54 & -0.74 & -0.22 & -0.75 & -0.56 \\ 0.04 & 1. & 0.45 & 0.41 & -0.03 & -0.4 & -0.44 & -0.28 & 0.16 \\ -0.67 & 0.45 & 1. & 0.39 & 0.49 & 0.2 & -0.16 & 0.15 & 0.35 \\ -0.4 & 0.41 & 0.39 & 1. & 0.06 & 0.2 & 0.11 & 0.13 & 0.38 \\ -0.54 & -0.03 & 0.49 & 0.06 & 1. & 0.36 & 0.02 & 0.16 & 0.39 \\ -0.74 & -0.4 & 0.2 & 0.2 & 0.36 & 1. & 0.37 & 0.57 & 0.19 \\ -0.22 & -0.44 & -0.16 & 0.11 & 0.02 & 0.37 & 1. & 0.11 & -0.25 \\ -0.75 & -0.28 & 0.15 & 0.13 & 0.16 & 0.57 & 0.11 & 1. & 0.57 \\ -0.56 & 0.16 & 0.35 & 0.38 & 0.39 & 0.19 & -0.25 & 0.57 & 1.\end{array}\right)$

I do not quite match them. In fact, we differ in one number, at the end of the first row (and at the end of the first column, of course). To five places, I have the number as -0.56492. They show -.57 where I round to -.56.

That’s irrelevant. What is not irrelevant is the result of computing the eigenvalues of the rounded correlation matrix.

It could be a big deal, but it isn't. Here be dragons, in either case. The point is that their apparent starting point is their printed (hence rounded) correlation matrix. (To be more precise: they clearly computed an eigendecomposition of the correlation matrix. I used their printed correlation matrix.) Whether I use theirs or mine, so long as it's rounded to 2 places, life is interesting.

Let’s just do our thing: get the eigendecomposition of the rounded correlation matrix... and look at the eigenvalues.

$latex \left(\begin{array}{l} 3.48828 \\ 2.14083 \\ 1.10125 \\ 0.992444 \\ 0.543472 \\ 0.379233 \\ 0.224842 \\ 0.133101 \\ -0.00344958\end{array}\right)$

I hope you took a deep breath right there. The smallest eigenvalue is negative. But the correlation matrix is supposed to be positive semi-definite. (Because it's of the form $latex X^T\ X\ $.)

Alarm bells should be ringing in your head: eigenvalues of a positive semi-definite matrix are non-negative. Where did that negative eigenvalue come from?

Presumably the smallest eigenvalue is very close to 0, and the negative number is numerical error.

Well, sort of, but we can say more. Here are the eigenvalues of the unrounded correlation matrix:

$latex \left(\begin{array}{l} 3.48715 \\ 2.13017 \\ 1.09896 \\ 0.994483 \\ 0.543218 \\ 0.383428 \\ 0.225754 \\ 0.13679 \\ 0.0000456251\end{array}\right)$

We see that the last one is very small but positive. The computed correlation matrix is positive definite. The problem comes from rounding off the correlation matrix.

But that must be positive definite, too, you cry?

Why?

Symmetry is not enough to guarantee positive definite.

This is just the tip of an iceberg. There was nothing special about rounding to 2 digits, nothing special about a correlation matrix. It is not trivial to manipulate a positive (semi-) definite matrix and guarantee that subsequent matrices are still positive (semi-) definite. But that's about all I’ll say about the numerical hassles.

As I said, the computed correlation matrix is, in fact, positive definite: its determinant and all its eigenvalues are positive. Mathematica® does just fine with it.

But the rounded correlation matrix – which is what they presented – is not positive definite: its determinant and one eigenvalue are negative.

So we now know two good reasons to provide data instead of just providing a correlation matrix: one, we can do more with the data; two, a rounded-off correlation matrix may not be positive semi-definite. And, bless them, they did provide the data.

Just this insight alone upgrades this to a very good example. And this negative eigenvalue was the "something interesting". We’ll see very shortly why it happened. (Perhaps you can guess.)

To summarize. The smallest eigenvalue of the correlation matrix is extremely close to zero, but non-negative, as it should be. The real problem is that the correlation matrix is almost singular (not of full rank); then the rounded correlation matrix is almost singular, too, but the smallest eigenvalue went to the other side of zero.

The lesson we have learned is: if the correlation matrix is barely of full rank, working from a rounded version of it could work out badly.

Now, why is the correlation matrix almost singular? I.e. why is the smallest eigenvalue so close to zero?

I swear I had no idea that this example would tie in so closely with recent posts. I knew that inadvertent reduction of rank was important, but I didn't have a clear reason why.

What might cause the smallest eigenvalue to go to zero? All we did was compute a correlation matrix. That is, all we did was implicitly center the columns.

Ah ha! Just what are the row sums of the raw data?

Here they are:

$latex row sums = \left(\begin{array}{l} 100. \\ 100.4 \\ 100. \\ 99.8 \\ 100.2 \\ 100.1 \\ 100.1 \\ 99.9 \\ 99.9 \\ 99.9 \\ 100.1 \\ 99.9 \\ 99.9 \\ 100. \\ 99.9 \\ 100. \\ 99.9 \\ 99.7 \\ 99.9 \\ 99.8 \\ 100.1 \\ 100. \\ 100. \\ 100.1 \\ 100.2 \\ 100.\end{array}\right)$

The min, mean, and max are 99.7, 99.9923, and 100.4 respectively.

They’re not constant, but they're awfully close to constant. Hence, the smallest eigenvalue of the correlation matrix isn't zero, but it's awfully close to zero. I explained here that making (edit: constant) non-zero row sums followed by centering the columns leads to constant zero row sums.

So: we just got a real-life example of the inadvertent loss of rank caused by using the correlation matrix on constant-row-sum data. The computed correlation matrix is positive definite but almost singular (determinant almost zero but positive, smallest eigenvalue almost zero but positive); and then because we were nearly singular, the rounded correlation matrix could fail to be positive definite, and in fact failed to be positive semi-definite.

Next, we will confirm that part of their analysis based on the correlation matrix.

If one worries about future weather forecasts, one worries about the future of one's own life. If one neglects to find weather for an important and upcoming event, one is neglectful of one's own circumstantial lifestyle. If one never checks weather, one is easygoing, accepting of life's mystery, but may be too distant from society.

What comparisons can you make to lifestyle and the lust for a weather forecast?

I believe otherwise. My belief of course is based on my canine interpretation of the data that I’ve gathered in past five years. My experiences and research proves a very strong correlation between loyalty and profit.

You see humans are not as loyal as dogs. They probably don’t have the strong gene of loyalty sitting on their chromosomes, while we dogs have not just one but a whole bunch of them squashing our chromosomes into submission. So who could be a better loyalty researcher than a dog…or your own Marketing Guru, Oorvi!

It’s my contention that loyalty is a profitable business for dogs as well as humans!

The View on Profitability from the Canine End:
Loyalty for me has always been extremely profitable. Not that I went about being loyal in order to generate profits…it just happened! But then, in the past five years, I’ve done all that a dog is expected to do. I’ve been selective in the choice of my chewies, I’ve warned them of intruders, I’ve done substantial work on licking their faces, and I’ve wagged my tail at all the right moments! So, you see, I’ve been loyal to Mercury and Cameo. Today among other things my assets include:

• An assortment of collars and bowls
• A beautiful collection of rugs
• A comfortable and cozy box
• A warm quilt
• A dog-mattress
• Half of Cameo’s side of the bed
• A fat wad of pocket money (undisclosed amount, convertible into juicy chicken legs any time I wish.)

My dear reader, it would interest you to know that before I checked into the loyalty ring, I had nothing but a festering shoulder to call my own! So from the loyal canine customer’s viewpoint, loyalty surely is profitable.

The View on Profitability from the Human End:
However, the statement “Loyalty is not correlated with profit” refers to the profitability of the loyalty-generator/creator entities and not to the “loyals”! So let’s talk about Cameo and see how my loyalty has led to his profitability.

• I sleep with Cameo to ensure that he stays awake most of the night – as I toss and turn; he tosses and turns! With both of us awake through the night, our house remains safe from burglars.
• Cameo doesn’t go on vacations, because he doesn’t want to leave his loyal little Oorvi behind. This saves him oodles of money…and his profitability increases.
• These two (Mercury n Cameo, who else) don’t buy expensive shoes, bed-sheets, and clothes; for they fear that I’d chew them up. Again…it saves them money.
• They don’t eat out often for I’ve got them eating out of my paws – again, money saved is money earned!

It's clear that in the above case, both parties profited from the human-canine loyalty bond. I thus prove that there is strong correlation between loyalty and profitability!

Q.E.D.

PS for the Human Readers:

If any of you is interested in digging beyond my canine interpretation, read some criticism of this negation of loyalty/profitability correlation at:

• What is loyalty? by Brian Woolf – Global Leader in Loyalty Marketing.
• Critical review of "The mismanagement of customer loyalty" by Dr. Doug Grisaffe, Asst. Professor of Marketing at University of Texas, Arlington.

So what's the difference between a "cause" and a "risk factor"? Risk factors sound like risks, which are bad, right?

Let's look at an example. What's the leading cause of car accident mortality?

• Reckless driving? Nope.
• Speeding? Nope.
• Getting distracted? Nope.
• Bad weather? Nope.

None of these things actually cause death. Car accident mortality is usually caused by bodily harm incurred when we're introduced to Newton's First Law of Motion, i.e. "A body in motion will remain in motion unless acted upon by an outside force", like a tree or another car!

Now you might argue that this is splitting hairs, but my point is that we need to be careful when talking about cause and effect. In order for something to be causative, we need to be able to link the series of events together with a clear relationship between them. For example:

• Serious bodily harm usually causes death because we lose too much blood and our internal organs fail, or our internal organs become too damaged to function

Straightforward, right? So back to our secondary factors:

• Speeding can increase the probability of an accident, and thus death, because you and the other drivers have less time to react to avoid a collision
• Bad weather can increase the probability of accident, and thus death, because reduced visibility / traction can prevent you from avoiding a collision

Still straightforward, right? If we analyze car accident rates, we'd expect that drivers who speed or drive recklessly would have higher mortality rates. We start with a plausible cause, and we can verify effect. If necessary, we can test our hypothesis in a controlled environment.

But say we notice that drivers with red cars also have higher mortality rates. Now what? We have effect, but what's the cause? Working backwards is dangerous - just because something is correlated, doesn't make it causative. For example, what happens if we ban red cars? Will we have fewer car accidents? Not likely. In this case, red cars may be correlated to personality types that are more likely to drive recklessly, rather than being causative in any way. Some people are going to drive recklessly regardless of car color. So red cars may not cause increased mortality, but they are a risk factor for increased mortality.

All of this is intuitive for car accidents, but what about diseases? If we look back at the American Heart Association web site information from above, how many causative factors are listed? None. How many correlated factors are listed? All of them. Oops...

Digging around a little, I couldn't find any major health sites that said XXX causes YYY, besides smoking causing lung cancer. But some certainly imply causation:

"Extensive clinical and statistical studies have identified several factors that increase the risk of coronary heart disease and heart attack."

Risk factors increase the risk of heart disease? I don't think so... What they should have said is "they've identified several risk factors that are associated with an increased risk of heart disease". It's a subtle but important difference.

"People with diabetes are two to four times more likely to develop cardiovascular disease due to a variety of risk factors"

"Due to" implies "because of" - which certainly implies cause and effect. Hmm...

The definition of a risk factor is:

"A risk factor is a variable associated with an increased risk of disease or infection. Risk factors are correlational and not necessarily causal, because correlation does not imply causation"

So by definition, risk factors don't cause anything. If diet and obesity were causative, they'd say so - but they don't. So why are they trying so hard to get us to control risk factors that may or may not be causes? That's a topic for a future post...

Risk factor != cause

Also, don't assume that major risk factors are more likely causative than minor risk factors. "Major" simply means that they're more strongly correlated. For example, yellow teeth are a major risk factor for lung cancer. So yellow teeth cause lung cancer?

[Content © 2008 SorryToConfuseYou.com, All Rights Reserved.]

In our spring school devoted to Arrow's economics, Menahem Yaari gave a talk  entitled "correlation and cooperation." It was about games as a model of people's behavior, and Yaari made the following points:

It is an empirical fact that people (players in a game)  act in a correlated way,

It is unscientific not to take this into account (although this is not taken into account in game theory and economics).

The prisoner's dilemma

A basic example in game theory (which also played a central part in Yaari's lecture) is the Prisoner's dilemma. Let's talk about this example a little, before getting to Yaari's claims. Here  is Wikipedia's description of the dilemma:

"Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies ("defects") for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act? "

And here is a more "personal" description from Stanford's online  Encyclopedia of Philosophy.

"Tanya and Cinque have been arrested for robbing the Hibernia Savings Bank and placed in separate isolation cells. Both care much more about their personal freedom than about the welfare of their accomplice. A clever prosecutor makes the following offer to each. 'You may choose to confess or remain silent. If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, they will go free while you do the time. If you both confess I get two convictions, but I'll see to it that you both get early parole. If you both remain silent, I'll have to settle for token sentences on firearms possession charges. If you wish to confess, you must leave a note with the jailer before my return tomorrow morning.' "

The matrix of payoffs is described by the following nice picture.

Sympathy 

Millions of words have been spoken and written on the prisoner's dilemma. One thing that I was always curious about is this: Why, when we hear about it, do we tend to sympathize with the prisoners? Don't we want them to serve a long time in prison for the crimes they committed?

One explanation is that when we are faced with the story we automatically identified with the prisoners, the heroes of the story. Another explanation is that we automatically tend to favour cooperation, and regard cooperation as morally superior. Or is it that we tend to favour efficiency and we dislike the non efficient equilibrium point. Still I regard our sympathy with the prisoners as a little puzzle.

 The sympathy for the prisoners in the prisoner's dilemma is almost as strange as the sympathy created for Tommy deVitto, the character played by Joe Pesci in "Goodfellas," and for the famous Clyde Barrow and Bonnie Parker.

Do we like the character played by Joe Pesci (left) from Goodfellas because he is a good son, and even uses his mother's kitchen knife for his work?

And arn't they lovable? (Clyde and Bonnie)

Yaari's point

Let's move now to the claim made by Menachem Yaari. He argues that, empirically, it is the case that players' behavior in games like the prisoner's dilemma is positively correlated. This claim assumes that we can a priori associate the strategies of one player with those of another player. But this is often the case. In various cases the strategies of all players can be described as: "compromise", "going to war." In such cases the claim about players' actions being positively correlated is meaningful.

In his talk Yaari discusses this claim, various difficulties and various connections with all sorts of cool stuff ("free will", Newcomb paradox, etc.). He then tries to analyze theoretic game solutions (basically Nash equilibrium), based on the positive correlation hypothesis.   

Yaari's claims and line of research are interesting, although it is not clear where they can go.

First, thanks mb, for your comment and research summary.  In fact, I was not trying to deny the strong correlation between poverty and child abuse and neglect. If anything, I was asking that we be honest about it. That correlation has been documented in several studies over the years. It’s one of the areas of research that I would argue certain social workers like to bury, because it can easily become so inflammatory. This is largely because so many people get confused and believe the correlation between poverty and child maltreatment means causation.  Poor people turn into bad people very quickly in the minds of some, and we social workers don't like it when that happens.

To assert causation is to claim a pure relationship between a variable and an outcome. It looks like this: if there is poverty, we can count on child abuse or neglect happening.  Without poverty, there should not be child abuse or neglect, unless another independent cause is proven to exist.  Correlation looks like this: if there is poverty or abuse/neglect, there is a greater chance that the other one will also be present, BUT we do not yet have enough information to know why exactly this is–we think it might be these factors. 

In terms of basic logic, and impact on our approach to clients, there is a huge difference between the two. It’s dangerous and discriminatory to say that poverty, in and of itself, causes child abuse and neglect.  This would mean that we should expect poor people, solely by virtue of being poor, to abuse and neglect their children. But this cannot be right, because poor people do not dependably abuse and neglect their children.  Some do, many do not.  And of course many wealthy people abuse and neglect their kids.  All of this means that we cannot say that poverty, by itself, causes child maltreatment, and that we should be aware that something other than poverty is involved in the cause or causes.  My original post on Political Action touched on how we social workers may be inclined to over-emphasize the technicalities of causation to protect against negative stereotyping.

As dangerous as negative stereotyping is, it’s equally harmful to ignore correlative research that troubles us or reinforces stereotypes, such as the correlation between poverty and child maltreatment. It’s unsurprising that more children are abused and neglected in high stress situations where resources are scarce. And we as social workers shouldn’t go hiding that correlation because we’re afraid the general public will be biased because they can’t figure out the difference between causation and correlation. Our job is to face the facts, as they really are, and solve the problems. Our job is also sometimes to undo bias created when people misinterpret research, or when research is poorly conducted, and not just try to avoid the research altogether.

One final note: the thing about correlations is that they really do not tell us exactly what the causes are. Most of the time they signify that the causes are multiple, complex, varied, and/or interrelated. That is to say that even if poverty and child abuse and neglect are linked, that does not disqualify other factors from contributing, or even causing, the abuse and neglect. Thus, higher visibility and lower empowerment of some low income families may very well play a role in the high rates of poor families being involved with CPS. In every state CPS runs a little differently, so even if the study above suggests that overexposure of impoverished families to mandatory abuse reporters did not happen in the regions surveyed, it may be part of what goes on in other areas of the country. Other related issues may play roles in increased attention to poor families as well–it is easier to scrutinize families with fewer resources, poor self-advocacy skills, less education, and the myriad of other disadvantages many (but not all!) lower income families face. Moreover, professional reporters may be more inclined to report lower-income families based on cultural or behavioral issues unrelated to safety that nonetheless cause the professional discomfort. Abuse can only be found if reports are made.  It’s possible abuse is found less frequently in higher income households because members of these homes present in a way that inspires confidence and therefore reports are never made.

I think the report’s discussion of the visibility of poor families is helpful, and it dispels some worries about discrimination, but it is still incomplete. It does not explore all of the opportunities for unfairness that can happen in the CPS reporting and investigation process. I also think it is problematic that the report suggests that just because the statistics of child abuse would be astounding if equal abuse was happening in wealthy and poor families, it cannot be happening. True, it is likely not happening to an equal degree across class lines, but wealthy people generally have more resources at their disposal to avoid scrutiny at all levels. In short, I think it’s premature, based on the research, to assume that bias plays no role in the large proportion of poor families that are involved with protective services. Unfairness is surely not the only cause of imbalance, but discrimination–intentional and systemic–may very well play some role. The point is we ought to keep researching to find out, right?

Thanks again to mb for your comment. You made a good point and my statements merited some clarification.

I like this "number crunching" as the book Super Crunchers puts it. Very inspiring. Who wouldn't love to do some "correlating"? It's totally logical, seemingly easy and yet very impressive. I guess the most difficult thing is to get all of the data. Get it semantical. Get enough data for a representational meaning.

College presidents from about 100 of the nation's best-known universities -- including six from Connecticut -- are calling on lawmakers to consider lowering the drinking age from 21 to 18, saying current laws actually encourage dangerous binge drinking on campus.       

The movement called the Amethyst Initiative began quietly recruiting presidents more than a year ago to provoke national debate about the drinking age. The Connecticut schools that have signed on are Trinity College, the University of Hartford, St. Joseph College, Fairfield University, the University of New Haven and Mitchell College in New London. (continued)

Despite the assertions of MADD that "twenty-one is working", the sad reality is that it isn't. When I was in college, the drinking laws were perhaps the biggest joke— nobody followed them. It was common for upperclassmen to procure alcohol for the freshmen and sophomores who had not yet reached the age of majority. I knew no one who was deterred from drinking by the drinking age of twenty-one.

This AP articles raises a number of significant issues:

(1) MADD's Statistics Don't Distinguish Between Correlation and Causation: MADD asserts that twenty-one is working because alcohol-related vehicular fatalities have decreased. However, that statement fails to account for other factors that have reduced fatalities, such as changing cultural attitudes and advances in safety engineering. In short, they try to portray correlation as causation. MADD cannot produce statistics that exclude other factors while solely accounting for the effects of "21". For example, it appears that there was much greater social tolerance of driving under the influence in the early '80s than there is today, in much the same way that cultural attitudes towards cigarettes have changed. Similarly, MADD cannot discount the effect that 25 years of engineering advances have had on fatalities.

(2) Rule of Law: Is the drinking age a real law, or a joke? The criminal law is only as good as the enforcement that stands behind it. A society that keeps unenforced laws on the books invites contempt for the rule of law. However, effective enforcement of the 21 drinking age is cost prohibitive, for the same reason that Prohibition could never be enforced.

(3) Efficient Use of Law Enforcement Resources: Law enforcement faces more pressing problems than rounding up America's alcohol-consuming collegian population. It is a waste of law enforcement resources. If MADD's real concern is alcohol-related fatalities they should press for enhanced DUI enforcement, not the prohibition of alcohol consumption by 18-21 year-olds.

(4) Civil Rights: The current drinking age raises very serious civil rights concerns. Our country trusts 18-21 year olds to have sufficient judgement to bear arms in the cause of liberty. Isn't it a contradiction in terms to assert that that a man has the maturity to die for his country, but can't drink a beer?

(5) Federalism: The use of the National Highway Traffic Safety Commission to strong-arm the states into increasing the drinking age, is a first-order example of federal over-reaching. Ultimately, this issues should be decided according to the moral standards of local communities, not the fiat of federal bureaucrats in Washington. Because they are closer to the people, state and local governments are better equipped to decide these kind of issues.

(6) Risk Mitigation & Prison Overcrowding: The risk mitigation strategy proposed by MADD has thus far focused on throwing people in jail and increasing penalties. This is incredibly inane, given the overcrowding in Connecticut's prisons. If MADD were truly serious about mitigating the risks of DUI, they would have long ago offered a plan to provide alternate transportation to the intoxicated.

Now if we see some price action in day terms, then it just marked the end of a very short lived uptrend. Hardly lasting two weeks-three weeks. Starting somewhere from July 2nd and ending on 13th August, it has set the stage for a fall.

Now is it a bear trap or a real fall, needs to be seen.[See figure 2,daily]

But now Gold is also falling.And that sounds like a good news. Why? Traditionally money siphoned off from capital markets landed either in oil or gold. So when gold rises it sounds alarm calls for capital markets.

And hence, a falling gold can often sound to be a welcome song for the bulls. Although, there may be a reasoning that oil/gold correlation accounts for this fall, but this is not it is. Oil and Gold hold tremendous positive correlation around ~0.8, but in short durations the correlation vanishes to arround 0.113. And thus, I wont really count this fall in gold as a selloff rally due to oil. But perhaps it may sound some reallocation in assets. Or in other words sector rotation.

Following on this fall in gold, dollar also rose on the back of a two week rally. So all in all, it might look that we might see some long term uptrend soon. But this is not to say that, life will return back to normal and the way it was before this mess. We have ushered into a long term, at least a decade long Commodity Bull Run, starting from 2006. And this might cool of anytime between 2015-2017. Which should be the time when the next fall in global economy comes in. [1988-Dow Jon falls,1996- Asian Crisis,2000-Dot Com,2008-Sub Prime, falls nicely into a 7-8 years pattern]

Signing off!

Jump a.ka. Soham

Academic Performance of

PMA Class 2008

A Research Paper

Submitted to the Faculty of the Graduate School,

University of the Cordilleras

In Partial Fulfillment of the Course, Methods of Research (Education 500)

By:

Unson, Claro Jr G

Suderio, Elmer B

Galit, Jenny Rose M

3^rd  Trimester, SY 2007-2008

TABLE OF CONTENTS

TITLE                                                                                                                               PAGE

Title Page--------------------------------------------------------------------------------------------           1

Table of Contents----------------------------------------------------------------------------------           2

Acknowledgement---------------------------------------------------------------------------------           5

Chapters

I.          The Problem-------------------------------------------------------------------------------         6

            Background of the Study----------------------------------------------------------------          6

            Theoretical/Conceptual Framework--------------------------------------------------         13

            Paradigm-----------------------------------------------------------------------------------           19

            Statement of the Problem/hypothesis-----------------------------------------------          21

II.         Design and Methodology-------------------------------------------------------------        23

            Research Design--------------------------------------------------------------------------         23

            Population and Locale of the Study--------------------------------------------------          24

            Data Gathering tools---------------------------------------------------------------------          26

            Data Gathering Procedures------------------------------------------------------------         26

            Treatment of Data------------------------------------------------------------------------           27

III.        Presentation, Analysis and Interpretation of Findings---------------------      31

            Level of Academic Performance in High School (HSGPA) --------------------       31

            The level of Performance in the Entrance Examinations-------------------—-         33

            The Level of Academic Performance of PMA Class 2008---------------------        34

            Relationship of GPA with HSGPA and CQT---------------------------------------         36

Regression Line Equation between HSGPA / CQT and GPA-----------------       38

Multiple Regression Equation----------------------------------------------------------         41

IV.       Summary, Conclusions and Recommendations-------------------   43

            Summary-------------------------------------------------------------------------------------         43

            Findings--------------------------------------------------------------------------------------          43       

Conclusions---------------------------------------------------------------------------------          44

            Recommendations------------------------------------------------------------------------         44

References------------------------------------------------------------------------------------------          46

List of Tables

Table 1:          Breakdown of PMA Class 2008----------------------------------------------        25

Table 2:          Level of High School Academic Performance----------------------------       27

Table 3:          Level of Cadet Qualification Test Performance--------------------------        28

Table 4:          Level of Academic Performance of the PMA Cl 2008------------------       28

Table 5:          Level of Academic Performance in High School-------------------------       31

Table 6:          Level of Performance in Entrance Examination--------------------------        33

Table 7:          Level of Academic Performance of PMA Class 2008---------------—-     35

Table 8:          Relationship of GPA with HSGPA and CQT-------------------------------       36

Table 9:          Correlations and Effects to the Dependent Variable--------------------       38

Table 10:        Regression Line Equation Bet HSGPA / CQT & GPA-------------------     39

Table 11:        Predicted GPA Using HSGPA as Predictor--------------------------------     41

Table 12:        Predicted GPA Using CQT as Predictor------------------------------------      42

Table 13:        Multiple Regression Equation-------------------------------------------------        43

Table 14:        Predicted GPA Using CQT and HSGPA as Predictors-----------------     43

List of Figures

Figure 1:         Paradigm of the Study--------------------------------------------------------            19

Figure 2:         Level of Academic Performance in High School----------------------           32

Figure 3:         Level of Performance in Entrance Examination-----------------------           34

Figure 4:         Level of Academic Performance of PMA Class 2008----------------         35

Figure 5:         GPA-HSGPA Scatter Diagram and Regression Line----------------          39

Figure 6:         GPA-CQT Scatter Plot and Regression Line--------------------------           40

Appendices:

A.        Letter to the Philippine Military Academy Registrar-----------------------------         48

B.        Research Tally Sheet on GPA, HSGPA and CQT of PMA Cl2008---------         49

C.        SPSS Analysis Results----------------------------------------------------------------            49

D.        Aerial Map of the Philippine Military Academy-----------------------------------          52

ACKNOWLEDGEMENT

We wish to extend our sincerest gratitude to the people who unselfishly extended their assistance, expertise and support to complete this undertaking:

            Dr. Ireneo T Hilario, the adviser, who patiently provided his guidance and professional critic to the researchers.

            Major Jose Dodjie C Belloga Jr, the PMA Registrar, for providing the needed data for the study, without question asked.

            To Mrs Liberty P Unson and Mrs Felimel Suderio for the all out logistical support, food supply, encouragement and understanding.

            To our families and friends who unselfishly provided the much needed moral support.

            To the University of Cordilleras library assistants, for the consideration and assistance in searching for our needed references.

            Most especially, we would like to express our fervent gratitude to the Almighty GOD for everything. Without HIM nothing can ever be accomplished. Thank You LORD.

                                                                                                The Researchers

CHAPTER 1

THE PROBLEM

Background of the Study

            National security is one of the greatest concerns of every country in the world. To protect its survival, every government has to set-up its own national defense infrastructure that will serve as its main protection against internal or external threat. Major events in history such as world wars, civil wars, insurgencies and terrorist attacks had compelled every government to strengthen their national defense system. One of the main components of this national defense system is the establishment of the Armed Forces, which is managed and led by trained and capable military officers that are adept in the art of war, conflict management, and strategic planning. Aside from the procurement of modern technology and updated defense infrastructure, the effectiveness of any Armed Forces would also depend much on the quality of its leaders; hence, many governments have developed a scheme of recruiting, training and educating qualified military officers to sustain its armed forces. In the Philippines, as provided by law, the primary provider of officers to its Armed Forces is the Philippine Military Academy (PMA).

The Philippine Military Academy (PMA) had already existed for more than a century, providing a regular pool of officers to the Armed Forces of the Philippines. The following account is the short history of the Philippine Military Academy (PMA):

     Looking back, the Philippine Military Academy began with the establishment of the Academia Militar on October 25, 1898 at Malolos, Bulacan by virtue of a decree issued by the first president of the young Philippine republic, General Emilio Aguinaldo. The Academia was a school that awarded its graduates regular commissions in the armed forces. The Academia existed up to 20 January 1899, when hostilities between the Americans and Filipinos erupted.

On 17 February 1905, an Officer's school of the Philippine Constabulary was established at the Walled City of Intramuros in Manila. Three years later, on 01 September 1908, the school was relocated to Baguio City, initially at Camp Henry T Allen, and subsequently at Teacher's Camp.

On 08 September 1926, the Philippine Legislature passed Act No. 3496 which renamed the school the ‘Philippine Constabulary Academy' and lengthened its course from nine months to three years with provisions to strengthen the faculty and revise its curriculum

On 21 December 1936, Commonwealth Act No. 1 (also known as the National Defense Act) was passed. The Law formally created the Philippine Military Academy and authorized it to confer a Bachelor of Science degree on its graduates after they successfully complete the four-year course.

The outbreak of World War II in December 1941 disrupted training at the Academy. Classes 1942 and 1943 were graduated ahead of schedule, and its members were assigned to combat units in Bataan and other parts of the country. Many perished in the war.

On 05 May 1947, the Academy reopened at Camp Henry T Allen. Due to the need for wider grounds, the Academy moved to its present site at Fort del Pilar in Loakan, some ten kilometers from downtown Baguio City. Fort del Pilar, named after the young hero of the battle of Tirad Pass, Gen Gregorio del Pilar, was developed into a military training institution with facilities and infrastructure required by a growing academy. Its pre-war, technically-oriented curriculum (having been patterned after that of the US Military Academy at West Point) was restored. In the 1960s, the curriculum underwent major changes, as socio-humanistic courses were added or strengthened to balance the techno-scientific disciplines, with a view towards providing a well-rounded education that was relevant to the needs of the growing AFP(The Academy Scribe: The Story, 2006, p.97).

To accomplish its mission, the Philippine Military Academy (PMA) is conducting a yearly competitive examination nationwide to select the most qualified applicants for cadetship. With the minimum requirement of being a high school graduate, Filipino citizen, single and has not sired a child, every interested aspirant can apply for free. In the 80’s and 90’s, the Philippine Military Academy (PMA) used the National College Entrance Examination (NCEE) as one of the screening tools before a candidate could be allowed to take the entrance examinations. Only those with NCEE ratings of not less than 85% were allowed to take the examinations. When the National College Entrance Examination (NCEE) was abolished in 1994, the Philippine Military Academy (PMA) has adopted the high school grade as its initial screening criteria. Debates on this basis boiled up because there were contentions that high school grades are not based on equal standards unlike the National College Entrance Examination (NCEE) which was conducted using the same set of test nationwide. As such, the implementation of high school grade screening was not done strictly; hence there were candidates who passed the CQT with high school grade of as low as 76%.

After the entrance examinations the initial poll of candidates shall undergo the medical and psychiatric tests at the AFP Medical Center where the number of applicants shall be trimmed down to the desired number which usually varies from 300 to 400 depending upon the declared cadet quota. Yearly cadet quota is determined by subtracting the total number of 1^st year, 2^nd year and 3^rd year cadets from 1,100. The result will be the quota for the year. The standard cadet ceiling every year is 1,100, which means that the Philippine Military Academy (PMA) can only accommodate a maximum of 1,100 cadets at any one time.

Recently, it is observed that fewer quality applicants are encouraged to take the entrance examinations or the Cadet Qualification Test.

For the past several years, there has been a considerable drop in the number of applications for cadetship. Applicants fluctuated from as many as 21,572 in 1999 to as low as 8,127 in 2002. The average number of applicants per year from 2002 to 2004 is 11,583. When the 85 percent high school general average was implemented recently, the number of applicants dropped to only 4,235. (Philippine Military Academy [PMA] Roadmap 2015, 2006, p.81)

The Philippine Military Academy (PMA) cited several factors why this phenomenon happened considering the perceived risk of lives and economic viability of becoming a soldier.

This may be caused by various external factors like the unattractiveness of the military profession, the lure of working abroad as nurses or IT professionals, the effect of competing schools offering full scholarships like the Philippine National Police Academy, Maritime Academy of the Asia and the Pacific, Philippine Merchant Marine Academy and others. However, one major internal factor that must be looked into is the effectiveness of the PMA marketing and promotions program, if there is any. If this is addressed properly then there is a big chance that the PMA will be able to entice more students to apply for PMA cadetship and increase it applicant base. (PMA Roadmap 2015, 2006. p. 70)

Aside from the decreasing number of applicants, the Philippine Military Academy (PMA) is also concerned with the decreasing success rate of the cadets. Success rate would technically mean as the number of cadets that graduates each year in just four years of cadetship. The Philippine Military Academy (PMA) claims that success rate of the cadets highly depends on the quality of raw materials that it acquired. A study conducted by the Office of the Cadet Admissions as indicated in the PMA Roadmap 2015 (2006) concluded that “The cause for the low success rate may be traced from the input which is low quality of cadets the PMA procured” (p. 78).  The quality of cadets can be determined by their high school academic performance and their CQT scores. Furthermore, the PMA Roadmap 2015 (2006) declared that “Considering all other factors constant, the more intellectually capable applicants will have better chances of surviving the four-year academic course should they be appointed as cadets” (p.78).

While it is true that the PMA really desires to attract as many applicants as possible, the institution is not yet disparate to admit low quality candidates, which suggests that the Philippine Military Academy (PMA) still prefers quality over quantity. Considering the low success rate and the dwindling number of quality applicants, the Philippine Military Academy (PMA) crafted several strategies and courses of actions. The Philippine Military Academy’s craving to recruit quality applicants prompted it to propose the following future plans. “To revise the sets of entrance examinations and admit only applicants with high school grades of not less than 90%” (PMA Roadmap 2015, 2006, p.78).

            The practical application of this study which is very significant to the stakeholders of the Philippine Military Academy (PMA) is to provide an up-to-date data, based on scientific method to establish a relationship between the Cadet Qualification Test (CQT) given to applicants and their academic performance; and to provide scientific basis for increasing or even eliminating the high school required grade by establishing a relationship between high school grades (HSGPA) and academic performance (GPA). If the research results can prove that there is a significant relationship between the cadets’ performance in the entrance examination with their overall performance in the Philippine Military Academy (PMA), then we can say that the entrance examination is still relevant. Moreover, if it is established by this study that high school grade has a significant relationship with the overall performance in the Philippine Military Academy (PMA), then high school academic performance could be a valid predictor of performance in the Philippine Military Academy (PMA); as such, the plan to raise the required high school grade to 90% is justified.  In short, the study would be able to provide a decision making tool for the Philippine Military Academy (PMA) Office of the Cadet Admission whether or not to pursue their plans to revise the entrance examination sets and to push for the increase of the required high school grades to 90%.

Aside from the practical application of this research, it will also contribute to the bodies of knowledge and theories that attempt to establish a relationship between intelligence testing which is represented by the Cadet Qualification Test (CQT) and high school grades to overall college performance. There are a lot of studies conducted outside the Philippines about these variables but very few are published in the local setting most especially on the Philippine Military Academy (PMA) cadets; as such, the researchers would like to prove whether or not those foreign based claims are also true locally.

In general, the researchers are interested on this topic because of the fact that a Philippine Military Academy (PMA) cadet is a full government scholar supported by people’s taxes and one Philippine Military Academy (PMA) cadet drop-out would mean a tremendous waste of people’s money. Considering the present economic dilemma of the Philippines, the government can’t afford to incur unnecessary wastage of funds. Aside from the consideration that everyone should be concerned about the taxes that they are paying; every Filipino should be concerned about the national security because the Philippine Military Academy (PMA) is significant factor in the country’s national defense system and in the maintenance of peace and order in the country. Peace and order would connote favorable environment for economic growth because it encourage investors to invest their capital on industries inside the country. Consequently, economic growth would bring employment to the Filipinos which will ensure good life and improved standard of living to every Filipino.

Theoretical/Conceptual Framework.

            This research is anchored on two (2) main concepts as related to academic performance. The first one is on the theory of intelligence testing; where it attempts to quantify human intelligence through tests. The second concept is on the quantified high school performance as related to college performance of students.

            Testing is a very old concept which traced its origin from ancient China. The Chinese attempted to measure abilities, skills and acquired knowledge of an individual as part of their criteria for civil service. “Evidence suggests that the Chinese has relatively sophisticated civil service testing program more than 4,000 years ago. Every third year in China, oral examinations were given to help determine work evaluations and promotion decisions” (Kaplan R.M. & Soccuzzo D.P., 2005, p. 12). Diverse topics were also known to be included in the Chinese tests. “By the Han Dynasty (206 B.C. -220 A.D.) the use of test batteries was quite common. These test is related to such diverse topics as civil law, military affairs, agriculture, revenue and geography” (Kaplan R.M. & Soccuzzo D.P.,2005, p. 13) In the early Greek civilization, testing was used as an adjunct to educational process and used to assess mastery of physical and intellectual skills. In 1890, James Mckeen Cattell, an American Psychologist introduced the term “Mental Test’ which was used in the annual test given to college students purposely to measure their mental ability. Not until the end of the 2^nd World War when the term Intelligence Quotient (IQ) was coined by Lewis Terman. “L.M. Terman of Stanford University had revised the Binet Test for the use in the United States. Terman’s revision was known as the Stanford Binet Intelligence Scale” (Kaplan R.M. & Soccuzzo D.P., 2005, p. 15). Initially, according to Barnes and Noble (2008), the scores were reported in terms of Mental Age, just as in the original. Later, mental age and chronological age were used to compute a new metric called the Intelligence Quotient, or I.Q.

An IQ according to Stern (as cited by Kaplan and Saccuso, 2005) is defined as “IQ uses a subject’s mental age in conjunction with his or her chronological age to obtain a ratio score. The ratio score presumably reflected the subject’s mental development” (p.257)

            At present, there are two (2) major types of standardized tests. The first one is the standardized test that attempts to measure and describe an individual’s mental abilities which is much related to one’s IQ; and the second is the one that attempts to measure and describe an individual’s personality. These two (2) types of tests are vastly used in profiling candidates for employment and for scholarships or admission to educational institutions. The Philippine Military Academy (PMA) uses both types of tests in screening applicants for entry in the academy.

The Philippine Military Academy (PMA) implements first the mental test or what they term as the intelligence test in the form of standardized Cadet Qualification Test (CQT). This test can be categorized as achievement test in high school because it measures how much the applicant learned in his four year stay in secondary school. According to Kaplan (2005), “Achievement tests attempt to assess what the person has learned following specific course of instruction (p. 317). In the same manner, CQT can be also categorized as an aptitude test because it measures the candidate’s potential for more learning. Santrock J.W. (2003) has defined aptitude test as “Aptitude Test predicts an individual ability to learn a skill or what the individual can accomplish with training” (p.393). Although the Cadet Qualification Test (CQT) measures how much the applicant has learned in high school, it also attempts to verify the applicants’ potentials for further learning in the academy. Finally, the Cadet Qualification Test (CQT) can also be categorized as scholastic assessment test because it is the candidates’ passport for a four year scholarship program.

Upon the publication of the Cadet Qualification Test (CQT) results, the top 1,000 or so applicants shall undergo the second set of tests which includes the personality testing together with the physical and psychological screenings. When the candi